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d ; | (6 or f'@) be =xfore | “ar 2) Slap — = a ee i! ——— Definite Asari 7... oe a: = co —[A@ ma = ror = (uG)ec)-G@4c) = uG)- ca) | ~[. a | 2 fhe dx = a) - uCa) i | —_ | a 7 —T Fe wiOlion wech~ a L se cosy de = (sin), = sin 2- sind = 4 ae : a y= Gane) = Gant) Gano) = - (a) = . 8 : zits = Chan Le SS 1) q n_¢ t ey, - — Tt tT (3 ; y= (2) = (4-0) 24 PMG GTS : ty f og x dy = (x lag, X20), = Ga) - fin x og Apa stent Dad frperties of Defisike “Inisqration i i § $0) dx = $c) dk j —la 3 1 ni 8 de = = [fais —| 4 } oe 4 _ 4 a 4 | 1 fi = = ~ { £Grb-0) d — (f@ dt = fie | | , y ‘ —_| ° | - ~~ _ ~ 4 Wa — | cat ® Adding © ond ©, J Die a loaite dante “fated > Analy palying King’s tale ay = . a cm oq ban =} 2T= id Co fana + ey ot da —"} (tq ots d. ——O xs f log 4 dy = [-Ode=0 "fe pte} ge [sine de 2 Nine (SH Adding @ and _—_ — Fi sinx _dxy ——© arf sina “Osx t sd sonaheen x sinae | @ex "Wena le Aang King’s Rule 21= ¥ Sine + Geox ly = Be = vial dati (G5) dx. VT Tanase Jes % 4 sinh) + Loe CE-2) 2t= 0 = Osx du _—— 2 a a + Tene Tz t | 4 | Fx TW &: dy = dy = : (osm de =1T | fds Sena pt Ae [sx J [cose + sinX in pz Fe Ty | f dy. = ( de (Jenn du = T ott dotx 44 [oon rerer-ak: 6 if fem] | ar] —= Pyare a in | “| lat dt —@ Selution: {00 = Ti “kh : | & fi@-= = fuk =u 4@). Zt for *t dt xf'@=o Ped & ed oe PALS ae fot \ut dul 7s Jon? > 4b 2x PP TICS aes sap yay [ECD = — "t tow du Xt Wax 2=0 ee eT] yw => £G642)-Gad=0 se ET oka (42) G24) 20 MCy gw get los tt Say. - 7 = dt | Qo pk “ICE 2+ 7 FO= 8 (4%. (asa £4 ot” 4+ Seludion = dx oc] £ wi) t¥asx ron fae of Ste Lack | —s he dy dy | .* i a J Qe {@- (Sj. = 2 Ye po {()~ Ely = 4 cectx VT 2 ws 2 i: a Ee LF ay. enol = tee (ten x | | ed 2a 2 Jay, | Lin Ices. | Jon 30 —tone = Chaat) - (2-1) Solution + |! fo) = @S x- Tao FQ) dt 8 8 £60 = (SH — Stead s HES ={27 £@ =-Sinn— Po) sahbo "GO = -esx—® _Aading @ and @, $+ £"G)= -fate dks feta _ H@s#'G= | ao I@ de | _— feet 6 —— Se SL FG) dx = [£60 dx. 2 | ge f Teecral de _ o —C*_ ” z { n — 2os xt1=9 => oye a ac § —_— ed ‘Wo ZL Wes gy “e\ | /* ‘ (lal dy = [lol dx Li 7H a gl Ey =i 3 (= "C= [ x 2est+1 0 => OSx> TF = F bel | = as 1 x qhosnsd -2+3 =14 | ICE 25. . [\\ froperty Solubion : “fe aie Lisinx dx * ! \x ll ie fol dx = 442404 Get) nic °| *§ 4! C Lasinx | dx * i = G-DM Ion r a 2 = ( (Coen addy + [osnx] due i Lasinx|! TED. tan cxf ) aT Salution : T [ daoc2n dy + r Casina} dx at dy + (Ody id 2 a mye : ail Bud > a osx dx= f esx | dx +m -dy + “ —2dx ; J 72 d Wie —_] ° Q +&- ls "F Neosx] de a “7 lol de : ]} 0 } *) ich anf Jb a @,, = GQ), =2: On S| | Tl St ale NS é {a St a 4 | | / ty one [fs = P77 sl [Peco de = i! f feo de, if “$Q@od= £00 | pe) en a Se Q ee _ on O if f Qa-x) =—FG0 Yoperty Lf, sina de = f log, cosa. dX = “8 log 2 | og 3 Derivation i {eq sin x dx. —-® i rule he aw log sin (10-2) dx. Tue J tg. sin 2x de i maw iw n= se => 2dx= dk | Ta= = Ahen += je Hx=0 then £=0 hiking & and @ - ha bg, sink ak 21- ft Coy. dine log, oox dx Ta= f lg, cin x de di ‘E j :|(Qhi= f lege Coin, coe.) dy 2 ez} log, tw dt x 4 “e MMe ‘a sin 2m \ du. oll 21= i loa. no 2—6 . or 21=1- 21 = fe ] ib &, log, Coelpew) de ps Adding Onl @,_ 21: f Clog Gea log Grose) dy log, CA-cs x) dy —9 ane * log, [C4-cos) Cras] dx S Pot Oet54 2x2 yg King’s vule 6 -_ z4 = ly Gos Gedy: 22= @) ly diitblig af logesinad “ i. ; te ‘loge Grex —@ 912 0 5.2) |= —Tw (9.2 _ as re 1m sink dea mek Ae ss TE x= 0 then sink = no sie ie) Tye Ahen_s s1—>h.% — fi : ae — ___a-* Py gest =F ly2 es : _ 5 + 40] | @ f Fades f EGre) de 08 f $6 da = é f#G5 be | 6 bre t be = = =i i. : ana -f £ Gee) dx : 7a = +} Eh Property it] [re £0) is periodic funchion uith fundamental pariod T=>£G+enD = ea) (i) { ‘ £60 de =n. f FG) de =A - is} 3T : Derivation: | c fadx = “¢ fc) de + + foddy s [ £60dy 4 + T £00 dy D — a = Sri t food = “p Landy sf £67) de + ‘t SCT) dy at “f£GsGer l Q o rey ; £G) dx = “p fedde ‘ £60 deg a “f 6) =ln't fod | J ous 5 rn «i a i fey dn = Gren) “f fed de [ar Fda = Pe Cunt) dy = comand f $60 de ——————_ mrt _ o. ° a os —_ — —— | am SSS Se 17] mi fain = nf fod de : Derivation J “h fo0 dx = wf fea de 7 — Q {G0 dx + (| FO) dx Oo. -f foo dx + *t foddx's of LOddx © a. 2 TICE it ——— wo aS. Solutions f = don wa don - T ca T= 100 Ganattan 2 mus ; - caren han Int wat ton ox ) de J sapkan 402) de £00) = tn x + ton 2x4 ton 3x +...4 ban 40% £60) = ton nhan 2a -.-+ kan 10% wr _, 2 7 “e pce = ; = a to [Grade FG) Lom#= ) © om TT... = peas T=t Ie 5. sie: wey Slukien:|| Chat a +5) dx > 24 xh tp fag sSa \+{tonaa® so 3 a 2 z Fs v1 Tes f Clazal +5) dx *t Cheals 5) dur 24 - ‘oe 40 as J tat chats hy 24 30 Oo a = 0 a - w®& T= locales Jae Geos Sayed ooe Ay (20-20-2450 ; Z As Gay 2) - Cased) 2 “ 2 aa fogs) -G ~ane Sn ) >24 XE es) fo) oO 4 fot assa\.((f aS a+ Na we ) : ra a vss)-(gtss) ea L Ca | | ling 14 Re, ye ce | N—> 00 G ) c = [ocrmf [2] / ee i aa | | Eien ation of Definite “Thtearation | ce8) < $@ < hd 1 yaad = * EGde < { hoods i _ a! os ® | m< f@< (2 de De (2% dx y) , 2 - ICE jo. ™% ™y, i __ Slution: ||Ty = fos Ginn) de bs fain: Cesex. ce es | een dy ty gs P 0 TN TE %>0 Rava sinner: % @s-Ginx) > @s% : f cos Ginx) “dx o> Teak LEA Sai uk Sunni of Series dee “li ce Gis fe (et £ = f fO0 d= lim bh Ya S £ Cath) ) J > @ a T=9 J tahere Lnh= b-a «|| 1 no, ho [rcemf os | f ae fo fe _Gouckion: * [2] 05) a t= (({4] poe live (/ | a es lide dan tf lat PhS a a OSS | = -4 S40 2 . 2 267 a stenet T= (C105) dna Mf Cros) de é A os -,) al T= -05 (o- (-©), os CE-0) | Te -0' = bw (C=) =|0 ACE 38. | - 1 aut = =: ba & —— = Solution: [= du=a_- | |g, % dot t Tz -f leg 2 du | ed) er yn + 2 z= 8 o a =z, = Sot log = =f poe eee T= 2 geet dt = 2 [2 -* dx dot = “ok e* “ak, T= ( xQxe*) du a6. TE x=e fren gcentet, 4 Yo Te x=e han e pies 4ethe Je Cre” 4, ~ Ler de T= Je e-a CE 26- Solwkion: \im ae + Gn) | ho nh Wt tin mz pete One ne On") lim rae 2\ (4 Vs - ae a Ca} poe Bs A Xv] \im 4. S ant \ Ss nen et Con reer we © then t-> 4 pen L [recene] foe [ 77 © |! Wall's Ebrroula. be © ‘ep sinh de 7 Was doe = (i. DGD (ns)... 1 @2 \ k od po baghios \. Gy) (Ch) (4)... 1@2) § Kei if nis odd t HEN ae 3 Zit hjeleen? @) “ec Sin_ ne dee me" esin dt = Cha mt) Crem. 8)... 4 @2 od JZ z Ch Gr2)Gn-4)... 2 | an eee GuCieed)Gn-8)).. 3k. suit ty’ and fh” are even NEN MEN ke 4 if -otheruise x er 
